Is there a better method to add uniform thickness to a curve pattern that has been converted into a mesh?
Maybe there's a simpler way but you could try with the Wireframe modifier:


Select your mesh, fill with F.
Give your object a Wireframe modifier. Enable Boundary, choose the Thickness you want.
Apply the modifier.
In Edit mode, select all and flatten with a SZ0.
Remove doubles with a W.
Delete the unwanted faces.
Work the angles.